Historically, dimple patterns for golf balls have had an enormous variety of geometric shapes, patterns, and configurations. Primarily, patterns are laid out in order to provide desired performance characteristics based on the particular ball construction, material attributes, and player characteristics influencing the ball's initial launch angle and spin conditions. Therefore, pattern development is a secondary design step that is used to achieve the appropriate aerodynamic behavior, thereby tailoring ball flight characteristics and performance.
Aerodynamic forces generated by a ball in flight are a result of its velocity and spin. These forces, which overcome the force of gravity, are lift and drag. Lift force is perpendicular to the direction of flight and is a result of air velocity differences above and below the rotating ball. This phenomenon is attributed to Magnus and described by Bernoulli's Equation, a simplification of the first law of thermodynamics.
Bernoulli's equation relates pressure and velocity where pressure is inversely proportional to the square of velocity. The velocity differential, due to faster moving air on top and slower moving air on the bottom, results in lower air pressure on top and an upward directed force on the ball. Drag is opposite in sense to the direction of flight and orthogonal to lift. The drag force on a ball is attributed to parasitic drag forces, which consist of form or pressure drag and viscous or skin friction drag. A sphere is a bluff body, which is an inefficient aerodynamic shape. As a result, the accelerating flow field around the ball causes a large pressure differential with high-pressure forward and low-pressure behind the ball. In order to minimize pressure drag, dimples provide a means to energize the flow field and delay the separation of flow, or reduce the low-pressure region behind the ball. However, the penalty for reducing pressure drag is skin friction. Skin friction is a viscous effect residing close to the surface of the ball within the boundary layer. The dimples provide an optimal amount of disturbance, triggering the laminar turbulent flow transition while maintaining a sufficiently thin boundary layer region for viscous drag to occur.
The United States Golf Association (U.S.G.A.) requires that golf balls have aerodynamic symmetry. Aerodynamic symmetry allows the ball to fly with a very small amount of variation no matter how the golf ball is placed on the tee or ground. Preferably, dimples cover the maximum surface area of the golf ball without detrimentally affecting the aerodynamic symmetry of the golf ball.
Many dimple patterns are based on geometric shapes. These may include circles, hexagons, triangles, and the like. Other dimple patterns are based in general on three of five existing Platonic Solids including Icosahedron, Dodecahedron, or Octahedron. Furthermore, other dimple patterns are based on hexagonal dipyramids. Because the number of symmetric solid plane systems is limited, it is difficult to devise new symmetric patterns. Moreover, dimple patterns based some of these geometric shapes result in less than optimal surface coverage and other disadvantageous dimple arrangements. Therefore, dimple properties such as number, shape, size, and arrangement are often manipulated in an attempt to generate a golf ball that has better aerodynamic properties.
A continuing need exists for a dimple pattern whose dimple arrangement results in a maximized surface coverage and desirable aerodynamic characteristics.